It is a measure of Andy Murray's self-belief rather than any perceived arrogance that, while he acknowledges it is "pretty amazing" to reach the semi-finals of the Australian Open without dropping a set, he considers it feasible to advance to ­Sunday's final without blemish.

Hubris? Hardly. Murray's tennis, while not perfect, has been of such high quality for most of the 10 hours he has spent in reaching today's semi-final against the Croat Marin Cilic that he is entitled to think he can maintain that level of excellence.

He has seen off the hobbling world No2, Rafael Nadal, as well as a pair of giants in the 6ft 8in (2.03m) qualifier Kevin Anderson and the 6ft 9in (2.06m) American prospect John Isner. None of those matches, nor his tussles with the Frenchmen Marc Gicquel and Florent Serra, has demanded his presence in a fourth set. Cilic, meanwhile, has toiled eight hours longer, enduring three five-setters to get within sight of the prize. That is a significant disparity in workload and form. Murray, without doubt, deserves to be favourite.

"It doesn't happen that often when a guy makes a semi-final of a slam without dropping a set," Murray said. "I would love to get to the final without dropping one, but it has been a great start."

Only four players in the Open era have completed a grand slam without giving up a set: Bjorn Borg at Wimbledon in 1976, Roger Federer here three years ago, and, in the French Open, Ilie Nastase in 1973, Borg in 1978 and 1980, and Nadal in 2008.

What to conclude from that? Of that illustrious group, Murray is probably philosophically (in a tennis sense) closest to Borg, whose reluctance to abandon the baseline was some times interpreted as a lack of adventure, when actually it was the ultimate in scientific pragmatism.

Murray has come in for similar criticism in the past and even, ludicrously, in this tournament – until he showed in his quarter-final against Nadal that such judgments are best made according to the demands of the moment. He did shy away from an obvious volley in the second set that would have saved him grief in the subsequent struggle but, thereafter, Murray increasingly came in behind his serve, as he sensed the Spaniard weakening. It was selective daring.

Now his instincts have put him within sight of his first grand slam. "Potentially, I am six sets away from doing that," he said. Nor does he see this final in isolation, as a goal in itself. Murray is taking a longer view. "I want to win more than one grand slam title but the first one will be the toughest," he said. "Now, I will focus on trying to win here but there is still a lot of tennis to be played."

There is history, too. Cilic did a number on Murray in the fourth round of the US Open last year, winning in straight sets, a result and a performance that the Scot to this day puts down to the injury he was carrying on his left wrist; he subsequently won two Davis Cup matches, and then took a six-week break.

Murray knew he had come close then to repeating his effort of the previous year, when he reached the US final. He had beaten Cilic three times, comfortably. This, he reckoned, was a blip. Now, he has said quietly but firmly, it is time to set the record straight. That alone gives this match an edge, although Murray is keen not to ramp up the tension. "Physically," he said, "I feel in a lot better shape compared to the US Open. It is going to be a tough match, regardless of what has happened in the past. Tennis matches can change from day to day. There is no point thinking about those other matches."

But he knows Cilic must be suffering from his exertions.

"I've played in the past at slams a lot of tennis. He has come through a couple of tough ones and will go for it. But it is important for me to stay focused at the start of the match and get ahead. Then maybe his head will go down a little bit.

"But he might be good for three or four sets and, if he plays his best, then the first few sets will be really tough."

That is the mental insurance, the hard-wired pro's reluctance to take anything for granted. The reality may be different; Murray has been ruthless in this tournament, waiting for the kill with admirable patience.

He did it against Isner, whose long legs gave up on him in the heat, and he did it against Nadal, whose big heart could not carry him through to the end of their contest. If Murray sees the slightest hint of Cilic wilting, he will do what his new friend, Ricky Hatton, once did so ­effectively: go for the knockout.